We give a principle in derived categories, which lies behind the classical Auslander–Reiten
duality and its generalized version by Iyama and Wemyss. We apply the principle to show …

Let A be an artin algebra over a commutative artin ring R and mod A be the category of
finitely generated right A-modules. A cycle in mod A is a sequence of non-zero non …

We introduce the concept of maximal orthogonal subcategories over artin algebras and
orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory …

We know that the model theory of modules leads to a way of obtaining definable categories
of modules over a ring R as the kernels of certain functors (RM od) op→ A b rather than of …

Let (R, m) be ad-dimensional commutative Noetherian local ring. Let M denote the
morphism category of finitely generated R-modules, and let S be the full subcategory of M …

Let (mod Λ′, mod Λ, mod Λ ″) be a recollement of module categories for artin algebras
Λ′, Λ and Λ ″. We provide a sufficient condition such that a glued torsion pair in mod Λ is …

We clarify the relation between the subcategory D hf b (A) of homological finite objects in D b
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …

Let A be a finite-dimensional Gorenstein algebra of finite CM-type. We show that the
Gorenstein derived category of A has Auslander–Reiten triangles. In this case, we otain a …

We establish a general method to construct triangle equivalences between the singularity
categories of (commutative and non-commutative) Gorenstein rings and the cluster …

In this paper, we study, for an artin algebra, the class LA (and RA) which is a full subcategory
of the category modA of finitely generated A-modules, and which consists of all …